All these years the Chinese Government has subjected their people to unfair laws and unhealthy processes.
People, each of you suffers from tyranny of that regime.

Fight for justice, fight for freedom, fight for democracy!

In the defaces and leaks in this day, we demonstrate our revolt to the Chinese system. It has to stop! We aren’t asking you for nothing, just saying to protest, to revolt yourself, to be the free person you always want to be! So, we are writing this message to tell you that you should protest, you should revolt yourself protesting and who has the skills for hacking and programming and design and other “computer things”

We are Anonymous.
We are Legion.
We do not forgive.
We do not forget.
Expect us.

Can they actually take down the "Great Firewall of China?"

Probably not. As Emil points out, the firewall is a "massive and complicated system," and he is certainly far more qualified to make that sort of judgement than I.